Multiple-input, multiple-output (MIMO) communications can significantly increase spectral efficiencies of wireless systems. Under idealized conditions, a capacity of the channel increases linearly with the number of transmit and receive antennas, Winters, “On the capacity of radio communication systems with diversity in a Rayleigh fading environment,” IEEE Trans. Commun., vol. 5, pp. 871-878, June 1987, Foschini et al., “On the limits of wireless communications in a fading environment when using multiple antennas,” Wireless Pers. Commun., vol. 6, pp. 311-335, 1998, and Telatar, “Capacity of multi-antenna Gaussian channels,” European Trans. Telecommun., vol. 10, pp. 585-595, 1999.
The possibility of high data rates has spurred work on the capacity achievable by MIMO systems under various assumptions about the channel, the transmitter and the receiver. The spatial channel model and assumptions about the channel state information (CSI) at the transmitter (CSIT) and the receiver (CSIR) have a significant impact on the MIMO capacity, Goldsmith et al., “Capacity limits of MIMO channels,” IEEE J. Select. Areas Commun., vol. 21, pp. 684-702, June 2003.
For most systems, the instantaneous CSIT is not available. For frequency division duplex (FDD) systems, in which forward and reverse links operate at different frequencies, instantaneous CSIT requires a fast feedback, which decreases spectral efficiency. For time division duplex (TDD) systems, in which the forward and reverse links operate at the same frequency, the use of the instantaneous CSIT is impractical in channels with small coherence intervals because the delays between the two links need to be very small to ensure that the CSIT, inferred from transmissions by the receiver, is not outdated by the time it is used.
These problems can be avoided by using covariance knowledge at the transmitter (CovKT). This is because small-scale-averaged statistics, such as covariance, are determined by parameters, such as angular spread, and mean angles of signal arrival. The parameters remain substantially constant for both of the links even in FDD or quickly-varying TDD systems. Therefore, such statistics can be directly inferred at the transmitter by looking at reverse link transmissions without the need for explicit feedback from the receiver. In cases where feedback from the receiver is available, such feedback can be done at a significantly slower rate and bandwidth given the slowly-varying nature of the statistics.
The use of covariance knowledge at the transmitter to optimize the transmitted data sequences, assuming an idealized receiver with perfect CSIR, has been described by Visotsky et al., “Space-time transmit precoding with imperfect feedback,” IEEE Trans. Inform. Theory, vol. 47, pp. 2632-2639, September 2001, Kermoal et al., “A stochastic MIMO radio channel model with experimental validation,” IEEE J. Select. Areas Commun., pp. 1211-1226, 2002, Jafar et al., “Multiple-antenna capacity in correlated Rayleigh fading with channel covariance information,” to appear in IEEE Trans. Wireless Commun., 2004, Simon et al., “Optimizing MIMO antenna systems with channel covariance feedback,” IEEE J. Select. Areas Commun., vol. 21, pp. 406-417, April 2003, Jorswieck et al., “Optimal transmission with imperfect channel state information at the transmit antenna array,” Wireless Pers. Commun., pp. 33-56, October 2003, and Tulino et al., “Capacity of antenna arrays with space, polarization and pattern diversity,” in ITW, pp. 324-327, 2003. Jul. 12, 2004.
However, in practical applications, the CSIR is imperfect due to noise during channel estimation.
MIMO capacity with imperfect CSIR is described for different system architectures, channel assumptions and estimation error models. Many theoretical systems have been designed for spatially uncorrelated (‘white’) channels. While these theoretical solutions give valuable insights, they do not correspond to the physical reality of most practical MIMO channels, Molisch et al., “Multipath propagation models for broadband wireless systems,” Digital Signal Processing for Wireless Communications Handbook, M. Ibnkahla (ed.), CRC Press, 2004. In practical applications, the channel is often correlated spatially (‘colored’), and the various transfer functions from the transmit antennas to the receive antennas do not change independent of each other.
For the case where the CSIT is not available and MMSE channel estimation is used at the receiver, pilot-aided channel estimation for a block fading wireless channel has been described by Hassibi et al., “How much training is needed in multiple-antenna wireless links?,” IEEE Trans. Inform. Theory, pp. 951-963, 2003. They derive an optimal training sequence, training duration, and data and pilot power allocation ratio.
The problems with a mismatched closed-loop system have also been described, Samardzija et al., “Pilot-assisted estimation of MIMO fading channel response and achievable data rates,” IEEE Trans. Sig. Proc., pp. 2882-2890, 2003 and Yoo et al., “Capacity of fading MIMO channels with channel estimation error,” Allerton, 2002. A data-aided coherent coded modulation scheme with a perfect interleaver is described by Baltersee et al., “Achievable rate of MIMO channels with data-aided channel estimation and perfect interleaving,” IEEE Trans. Commun., pp. 2358-2368, 2001.
Baltersee et al., analyze the achievable rate of a data-aided coherent coded modulation scheme with a perfect interleaver. Mutual information bounds for vector channels with imperfect CSIR are described by Medard, “The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel,” IEEE Trans. Inform. Theory, pp. 933-946, 2000.
Others, in different contexts, state that orthogonal pilots are optimal, Guey et al., “Signal design for transmitter diversity wireless communication systems over Rayleigh fading channels,” IEEE Trans. Commun., vol. 47, pp. 527-537, April 1999, and Marzetta, “BLAST training: Estimating channel characteristics for high-capacity space-time wireless,” Proc. 37th Annual Allerton Conf. Commun., Control, and Computing, 1999.
Data covariance for spatially correlated channels, given imperfect CSIR, are described by Yoo et al., “MIMO capacity with channel uncertainty: Does feedback help?,” submitted to Globecom, 2004. However, the imperfect channel estimation was modeled in an ad-hoc manner by adding white noise to the spatially white component of channel state. Therefore, that model is inappropriate for many applications.
Lower and upper bounds on capacity are described for spatially white channels, Marzetta et al., “Capacity of a mobile multiple-antenna communication link in Rayleigh flat fading,” IEEE Trans. Inform. Theory, vol. 45, pp. 139-157, January 1999. Those systems do not assume any a priori training schemes for generating the CSIR, and serve as fundamental limits on capacity.
Prior art systems either do not exploit statistics knowledge completely to determine the pilot and data sequences, or either design only pilot or only data signals, but not both, and make idealized assumptions about the channel knowledge at the transmitter and/or the receiver.
In light of the problems with the prior art MIMO systems, it is desired to generate optimal pilot and data signals, even when the instantaneous and perfect channel state is unavailable at the transmitter and receiver.